The goal of this course is to teach students basic concepts and theoroms from the following areas: Probability Theory, Mathematical Statistics and Methods of Deriving Empirical Formulae.

The outcome

This course provides knowledge that can be applied to other natural science and technical-technological courses taught in the department. The course is intended to enable students to successfully apply the acquired mathematical knowledge in solving techical and technological problems, as well as in mathematical processing of experimental data. ;

Contents

Contents of lectures

Probability – definition, characteristics, total probability theorem, Bayes’ theorem, random variable, the most important discrete and continuous probability distributions, multidimensional random variables, the most important multidimensional distributions, numerical characteristics of distributions, numerical characteristics of multidimensional distributions, law of large numbers and central limit theorem of the calculus of probabilities; Statistics – random sample, examples of the most important statistics, tabular and graphical representation of statistical data, point estimation of distribution parameters, methods of obtaining point estimations , confidence intervals for parameters of normal distribution , parametric hypothesis testing, non-parametric tests, regression (linear, non-linear, multidimensional). Solving examples and tasks that illustrate various concepts presented in the theoretical contens as well as their mutual relations. Moreover, the practical examples give an opportunity to exercise applying acquired theoretical knowledge to problems of natural and technical-technological sciences.